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Chapter 3: Problem 24

Little Italy Pizza charges \(\$ 12.00\) for a 12 -inch diameter sausage pizza and \(\$ 14.00\) for a 14 -inch diameter sausage pizza. Write the pseudocode algorithm that calculates and displays how much each of these earns the establishment per square inch of pizza sold. (Hint: you will need to first calculate how many square inches there are in each pizza.)

Short Answer

Expert verified
Answer: Little Italy Pizza earns approximately: - \(\frac{1}{3\pi}\) dollars per square inch for the 12-inch sausage pizza - \(\frac{2}{7\pi}\) dollars per square inch for the 14-inch sausage pizza

Step by step solution

01

Identify the given information

We are given the prices and diameters of the following sausage pizzas: - 12-inch diameter pizza costs $12.00 - 14-inch diameter pizza costs $14.00
02

Calculate the area of each pizza

To find the area of each pizza, we need to use the formula for the area of a circle: Area = π × (radius)^2 First, we need to convert the diameters to radii. The radius is half of the diameter, so: - Radius of 12-inch pizza: 12/2 = 6 inches - Radius of 14-inch pizza: 14/2 = 7 inches Now, we can calculate the areas: - Area of 12-inch pizza: π × (6)^2 = 36π square inches - Area of 14-inch pizza: π × (7)^2 = 49π square inches
03

Calculate the earnings per square inch for each pizza

To find the earnings per square inch, we will divide the price of each pizza by its respective area: - Earnings per square inch for 12-inch pizza: \(\frac{12}{36\pi} = \frac{1}{3\pi}\) - Earnings per square inch for 14-inch pizza: \(\frac{14}{49\pi} = \frac{2}{7\pi}\)
04

Display the results

The final step is to display the earnings per square inch for each pizza: - Earnings per square inch for 12-inch pizza: \(\frac{1}{3\pi}\) dollars - Earnings per square inch for 14-inch pizza: \(\frac{2}{7\pi}\) dollars

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